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MATHEMATICS OF CARYATIDS
Lefteris Kaliambos 13 November 2018 Τhe name Caryatid was given to an architectural column which takes the form of a standing female figure. The first examples come from ancient Greek architecture and indeed, the most celebrated examples are found in the south porch of the Erechtheion on the acropolis of Athens. This building was constructed between 421 and 406 BCE as part of Pericles’ great project to rejuvenate the architecture of the great city. Scholars believe them to be carved by different artists, most probably from the workshop of Alcamenes, student and colleague of Pheidias. Today under my detailed researches of the golden section in the architectures of ancient Greece I have found that in Caryatids of Erechtheion and also in the two Caryatids of my discovery of the Hephaestion tomb in Amphipolis the height H of each Caryatid compared with the height h of the analogous pedestal is given by the relation H/h = (Η+h)/H = Φ = (1+50.5)/2 = 1.618034 Although the golden number Φ = 1.618034 of the golden section was taken from the first letter of Pheidias (Φειδίας) unfortunately in the absence of a detailed knowledge about the math of the golden ratio neither was able to reveal the golden ratio of Caryatids. For example in my discovery of the mathematical tomb of Hephaestion in Amphipolis the height H = 2.27 m and the height h = 1.40 m of the Caryatids and the pedestals respectively as measured and announced by the excavators in Amphipolis, in the absence of a detailed knowledge about the math of the golden section the excavators in Amphipolis did not know that the relation 2.27/1.40 = 1.62 gives the golden number Φ = 1.62. In fact, it was applied by the architect Dinocrates following the math of Caryatids in the Erechtheion. Under this condition using a combinatory method like the British architect Ventris who deciphered Linear B, I was able to reveal not only the golden section of the two Caryatids in the mathematical tomb of Hephaestion but also the same mathematics in the Caryatids of the Erechtheion. Purposely I present here a suitable photo of the Erechtheion with Caryatids of the same height H in which one can see also the analogous pedestals with the same height h.' ' ΜΥ DISCOVERΥ OF THE GOLDEN SECTION IN THE TWO CARYATIDS OF THE HEPHAESTION TOMB IN AMPHIPOLIS In my discovery of the mathematical tomb of Hephaestion in Amphipolis , I revealed not only the Hellenistic stadion (unit of length) or the so-called itinerary stadion = 157.5 m but also the math used by Denocrates on the golden section in the lion, in sphinxes, and in Caryatids. Specifically, there are two female statues in the type of Caryatids who support the entrance to the second chamber of the tomb. According to the measurements made by the excavators the height H of each Caryatid is H = 2.27 m, while in their pedestals the height h is h = 1.40 m. So the total height H + h = 3.67 m. Here we observe that both the ratio H/h = 2.27 / 1.4 = 1.62 and the ratio (H + h) / H = 3.67 / 2.27 = 1.62 give us the same approximation of the number Φ of the golden section given by the relationship Φ = (1 + 50.5 ) / 2 = 1.618034 As we know according to the mathematics of the golden section if h = 1 ( unit of length) we get H = Φ= 1.62. Then we will have H/h = (H + h) / H = Φ / 1 = (Φ + 1) / Φ Or Φ 2 = Φ + 1 or Φ 2 - Φ -1 = 0 Here we have to do with a quadratic equation where the value of the variable Φ will be given by the solution of the equation. That is Φ = (1 + 5 0.5 ) / 2 = 1.618034 Thus, Dinokrates starting from the total height (H + h) = 3.67 m was able to determine the heights H and h as follows (H + h) / H = Φ or H = 3.67 / 1.618034 = 2.268 m or roughly H = 2.27 m and h = 3.67 - 2.27 = 1.4 m DISCOVERY OF THE GOLDEN SECTION IN CARYATIDS OF ERECHTHEION On the north side of Erechtheion there is a large porch with six Ionic columns, and on the south, the famous "Porch of the Maidens", with six draped female figures (caryatids) as supporting columns. The porch was built to conceal the giant 15-ft beam needed to support the southwest corner over the Kekropion, after the building was drastically reduced in size and budget following the onset of the Peloponnesian war. The best-known and most-copied examples are those of the six figures of the Caryatid Porch. One of those original six figures, removed by Lord Elgin in the early 19th century, is now in the British Museum in London. The Acropolis Museum holds the other five figures, which are replaced onsite by replicas. The five originals that are in Athens are now being exhibited in the new Acropolis Museum, on a special balcony that allows visitors to view them from all sides. The pedestal for the Caryatid removed to London remains empty. From 2011 to 2015, they were cleaned by a specially constructed laser beam, which removed accumulated soot and grime without harming the marble's patina. Each Caryatid was cleaned in place, with a television circuit relaying the spectacle live to museum visitors. Although of the same height = 2.31 meters and build, and similarly attired and coiffed, the six Caryatids are not the same: their faces, stance, draping, and hair are carved separately; the three on the left stand on their right foot, while the three on the right stand on their left foot. Their bulky, intricately arranged hairstyles serve the crucial purpose of providing static support to their necks, which would otherwise be the thinnest and structurally weakest part. Using the same method as that of the two caryatids in the Hephaestion tomb I discovered that the height H = 2.31 m of each Caryatid in Erechtheion compared with the height h = 1.43 m of each pedestal gives the ratio Φ = (1+50.5) /2 = 1.618034. That is (H +h)/H = Φ = H/h Or (2.31 + 1.43) / 2.31 = (1+ 50.5)/2 = 2.31/1.4 3 To conclude I emphasize that the math of the golden section was used not only in Caryatids but also in the architecture of the Parthenon in which the math is related with the math of the Great Pyramid in Egypt. (PARTHENON MATH AND GREAT PYRAMID).